A reflected forward-backward splitting algorithmic framework
Optimization and Control
2026-05-19 v1
Abstract
In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and Lipschitz continuous operators. We provide a unified convergence analysis under mild conditions, eliminating the need to analyze the convergence of each algorithm individually. The heuristic strategies for matrix selections are proposed through a numerical experiment, based on which a new algorithm is derived. A further numerical experiment on the regularized saddle-point problem is then presented to demonstrate the effectiveness of the proposed algorithm.
Cite
@article{arxiv.2605.17731,
title = {A reflected forward-backward splitting algorithmic framework},
author = {Haowen Zheng and Yongyu Fu and Qiao-Li Dong and Shuangbao Li},
journal= {arXiv preprint arXiv:2605.17731},
year = {2026}
}